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If R is a relation defined as aRb, "iff"...

If R is a relation defined as aRb, `"iff"|a-b|gt0`, then the relation is

A

reflexive

B

symmetric

C

transitive

D

symmetric and transitive

Text Solution

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The correct Answer is:
D
Since, R is defined as aRb, iff `|a-b| gt 0.`
Reflexive aRa, iff `|a-a| gt 0,`
Which is not true. So, R is not reflexive.
Symmetric aRb, iff `|a-b| gt 0`
Now, bRa iff, `|b-a| gt 0`
`because |a-b| gt 0 rArr |b-a| gt 0`
`therefore bRa`
Thus, R is symmetric.
Transitive aRb, iff `|a-b| gt 0`
bRc, iff `|b-c| gt 0`
`rArr |a-b+b-c| gt 0`
`rArr |a-c| gt 0`
`therefore aRc`
Thus, R is also transitive.
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